Firefighter Practice Exam

What quantity of distilled water needs to be added to 5 liters of 100% alcohol to obtain a 75% alcohol solution?

1. 1 liter

2. 2 liters

3. 3 liters

4. 4 liters

The correct answer is: 2 liters

To determine how much distilled water needs to be added to 5 liters of 100% alcohol to achieve a 75% alcohol solution, it's essential to first understand the relationship between the volume of alcohol and the desired concentration. Initially, there are 5 liters of pure alcohol, which consists of 100% alcohol. When you want to dilute this to a solution that is 75% alcohol, the total volume of the solution must contain a certain amount of pure alcohol. The goal is to maintain 75% of the total solution as alcohol. If we let \( x \) be the volume of distilled water added, the total volume of the solution becomes \( 5 + x \) liters. The effective volume of alcohol in this solution remains at 5 liters because we haven't changed the amount of alcohol, only diluted it. To find the correct amount of water to add, set up the equation that represents the setup: \[ \frac{\text{Volume of alcohol}}{\text{Total volume of solution}} = \text{Desired concentration} \] Substituting the known values: \[ \frac{5}{5 + x} = 0.75 \] Now, solve for \( x \): 1